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Mixed Zero-Sum Stochastic Differential Game and Doubly Reflected BSDEs with a Specific Generator

Author

Listed:
  • Brahim El Asri

    (ENSA)

  • Nacer Ourkiya

    (ENSA)

Abstract

This paper studies the mixed zero-sum stochastic differential game problem. We allow the functionals and dynamics to be of polynomial growth. The problem is formulated as an extended doubly reflected BSDEs with a specific generator. We show the existence of solution for this doubly reflected BSDEs and we prove the existence of a saddle-point of the game. Moreover, in the Markovian framework we prove that the value function is the unique viscosity solution of the associated Hamilton–Jacobi–Bellman (HJB) equation.

Suggested Citation

  • Brahim El Asri & Nacer Ourkiya, 2024. "Mixed Zero-Sum Stochastic Differential Game and Doubly Reflected BSDEs with a Specific Generator," Dynamic Games and Applications, Springer, vol. 14(3), pages 549-577, July.
    • Handle: RePEc:spr:dyngam:v:14:y:2024:i:3:d:10.1007_s13235-023-00515-w
    DOI: 10.1007/s13235-023-00515-w
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    References listed on IDEAS

    as
    1. Bahlali, Khaled & Hamadène, SaI¨d & Mezerdi, Brahim, 2005. "Backward stochastic differential equations with two reflecting barriers and continuous with quadratic growth coefficient," Stochastic Processes and their Applications, Elsevier, vol. 115(7), pages 1107-1129, July.
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